i wish i could help with the problem as it seems most frustrating, but i can tell you that Windows recognizing it as a CD drive is perfectly "normal."
i say normal in quotes because it's par for the course for windows and doesn't affect functioning of the product, but it's annoying as all hell if you're very detail oriented like myself. you'd think micro$oft could manage to correctly recognise attached devices!
out of pure curiousity, how old is the dvd drive in question? also, is it at all possible for you to test another drive in your system? even a spare dvd-rom hanging around or maybe one of the roomies will be daring enough to let you take their computer apart and give it a shot? that would at least determine if it was something on your system that isn't a 24 fan or if it's the drive itself.
if that series is the only thing you're having trouble with I wouldn't worry too much (easy to say, right?), but if you start having trouble with a wider variety of discs i'd consider replacing the drive. a brand new dvd burner can be had probably for less than you paid for that season of 24. i just bought a benq dw 1655 with lightscribe for ~$40.
replacement shouldn't have to be the option, but if you keep running into trouble i'd keep an eye on the bargain basement forums for some good deals.
what i was getting at when asking about the age of the drive is if it's very new you could get a replacement under warranty or if it's very old maybe the laser is wearing out (less likely since you said these discs are the ONLY problems you've had)
not very helpful, i know, but i definitely empathize with you. I'm a girl and I have 6 (male) roommates so TV time (not to mention bathroom time) is a precious commodity